[Luo, Ziren] Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China
; [Lau, Y. K.] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
; [Pei, Shouyong] Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China
; [Gong, Xuefei] Chinese Acad Sci, Inst High Energy Phys, Theoret Phys Ctr Sci Facil, Beijing 100049, Peoples R China
; [Yang, Ran] Huazhong Univ Sci & Technol, Dept Phys, Wuhan 430074, Peoples R China
Single photon Sagnac interferometry as a probe to macroscopic quantum mechanics is considered at the theoretical level. For a freely moving macroscopic quantum mirror susceptible to radiation pressure force inside a Sagnac interferometer, a careful analysis of the input-output relation reveals that the particle spectrum readout at the bright and dark ports encode information concerning the noncommutativity of position and momentum of the macroscopic mirror. A feasible experimental scheme to probe the commutation relation of a macroscopic quantum mirror is outlined to explore the possible frontier between classical and quantum regimes. In the Appendix, the case of Michelson interferometry as a feasible probe is also sketched.